Chat messages previously lived only in React state and vanished on
navigation or refresh. Persist each conversation as a session in
localStorage and add a sidebar to switch between, restore, or delete
past chats, matching the pattern of the account page's client-side
persistence.
Claude-Session: https://claude.ai/code/session_012RrMZ8Y9BhuMkKNcw2bakZ
Co-authored-by: Claude <noreply@anthropic.com>
